def get_stability_condition(plot_results=True):
current_factors = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
colors = cm.copper(np.linspace(0.0, 1.0, len(current_factors)))
# Get profiles
dat = np.loadtxt(os.path.join('input_profiles.dat'))
# Modify and plot input profiles
r = dat[:, 0]
R = dat[:, 1]
j_phi = dat[:, 2]
B_z = dat[:, 3]
B_theta = dat[:, 4]
psi_n = dat[:, 5]
r_to_psin = interpolate.interp1d(r, psi_n)
psin_to_r = interpolate.interp1d(r, psi_n)
q = r * B_z / (R * B_theta)
q[0] = q[1]
if plot_results:
fig, ax = plt.subplots(2, 2, figsize=(10, 10), sharex=True)
ax[0, 0].plot(r, B_z, c='k')
ax[0, 0].set_ylabel('$B_{\phi}$ [T]', fontsize=fontsize)
ax[1, 0].plot(r, B_theta, c='k')
ax[1, 0].set_ylabel('$B_{\\theta}$ [T]', fontsize=fontsize)
for i, factor in enumerate(current_factors[::-1]):
linestyle = '--' if i > 0 else '-'
ax[0, 1].plot(r,
factor * j_phi * 1e-3,
linestyle=linestyle,
c=colors[i])
ax[0, 1].set_ylabel('$j_{\phi}$ [kA]', fontsize=fontsize)
ax[1, 1].plot(r, q, c='k')
ax[1, 1].set_ylabel('q', fontsize=fontsize)
ax[1, 1].set_xlabel('r [m]', fontsize=fontsize)
ax[1, 0].set_xlabel('r [m]', fontsize=fontsize)
ax[0, 0].set_xlim([0.0, 1.0])
fig.tight_layout()
plt.savefig('input_profiles')
plt.show()
r_max = r[-1]
deltas = list()
alphas = list()
for factor in current_factors:
j_phi_sim = j_phi * factor
solver = TearingModeSolver(m,
r,
r_max,
B_theta,
B_z,
j_phi_sim,
q,
num_pts,
delta=1e-12)
solver.find_delta(plot_output=False)
psin_lower = r_to_psin(solver.r_lower)
psin_upper = r_to_psin(solver.r_upper)
if plot_results:
fig, ax = plt.subplots(2, sharex=True)
ax[0].plot(psin_lower,
solver.psi_sol_lower[:, 0],
label='solution from axis')
ax[0].plot(psin_upper,
solver.psi_sol_upper[:, 0],
label='solution from boundary')
# Plot comparison solution if it exists
validation_file = 'flux_validation_vc_{}.csv'.format(factor)
if os.path.exists(validation_file):
flux_validation = np.loadtxt(validation_file, delimiter=',')
flux_validation[:, 1] /= np.max(flux_validation[:, 1])
flux_validation[:, 1] *= np.max(solver.psi_sol_lower[:, 0])
ax[0].plot(flux_validation[:, 0],
flux_validation[:, 1],
linestyle='--',
label='JOREK')
ax[0].set_ylabel('$\Psi_1$', fontsize=fontsize)
ax[0].legend()
ax[0].set_xlim([0.0, 1.0])
ax[1].plot(psin_lower, solver.psi_sol_lower[:, 1])
ax[1].plot(psin_upper, solver.psi_sol_upper[:, 1])
ax[1].set_ylabel('$\\frac{\partial \Psi_1}{\partial r}$',
fontsize=fontsize)
ax[1].set_xlabel('$\hat \Psi$', fontsize=fontsize)
plt.show()
deltas.append(solver.delta)
alphas.append(1 - factor)
np.savetxt('deltas', np.asarray(deltas))
plt.figure()
plt.plot(alphas, deltas)
plt.axvline(0.346,
linestyle='--',
color='grey',
label='Linear stability boundary')
plt.axvline(0.25,
linestyle='--',
color='g',
label='JOREK stability boundary')
plt.grid(linestyle='--')
plt.ylabel('$\Delta\'$', fontsize=fontsize)
plt.xlabel('$\\alpha$', fontsize=fontsize)
plt.legend()
plt.xlim([0.0, 1.0])
plt.savefig('current_stability_{}'.format(m))
plt.show()
def get_stability_condition(plot_results=True):
current_factors = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.65, 0.675, 0.6875, 0.7, 0.8, 0.9, 1.0]
colors = cm.copper(np.linspace(0.0, 1.0, len(current_factors)))
# Get profiles
dat = np.loadtxt(os.path.join('input_profiles.dat'))
# Modify and plot input profiles
r = dat[:, 0]
R = dat[:, 1]
j_phi = dat[:, 2]
B_z = dat[:, 3]
B_theta = dat[:, 4]
psi_n = dat[:, 5]
r_to_psin = interpolate.interp1d(r, psi_n)
psin_to_r = interpolate.interp1d(r, psi_n)
q = r * B_z / (R * B_theta)
q[0] = q[1]
if plot_results:
fig, ax = plt.subplots(2, 2, figsize=(10, 10), sharex=True)
ax[0, 0].plot(r, B_z, c='k')
ax[0, 0].set_ylabel('$B_{\phi}$ [T]', fontsize=fontsize)
ax[1, 0].plot(r, B_theta, c='k')
ax[1, 0].set_ylabel('$B_{\\theta}$ [T]', fontsize=fontsize)
for i, factor in enumerate(current_factors[::-1]):
linestyle = '--' if i > 0 else '-'
ax[0, 1].plot(r, factor * j_phi * 1e-3, linestyle=linestyle, c=colors[i])
ax[0, 1].set_ylabel('$j_{\phi}$ [kA]', fontsize=fontsize)
ax[1, 1].plot(r, q, c='k')
ax[1, 1].set_ylabel('q', fontsize=fontsize)
ax[1, 1].set_xlabel('r [m]', fontsize=fontsize)
ax[1, 0].set_xlabel('r [m]', fontsize=fontsize)
ax[0, 0].set_xlim([0.0, 1.0])
fig.tight_layout()
plt.savefig('input_profiles')
plt.show()
r_max = r[-1]
deltas = list()
gammas = list()
alphas = list()
if os.path.exists(data_output):
alphas = 1 - np.asarray(current_factors)
deltas = np.loadtxt(data_output)
gammas = np.loadtxt(gamma_output)
else:
for factor in current_factors:
j_phi_sim = j_phi * factor
solver = TearingModeSolver(m, r, r_max, B_theta, B_z, j_phi_sim, q, num_pts, delta=1e-12)
solver.find_delta(plot_output=False)
solver.get_gamma()
# Transform to psi_norm for comparison with JOREK
psin_lower = r_to_psin(solver.r_lower)
psin_upper = r_to_psin(solver.r_upper)
if plot_results:
fig, ax = plt.subplots(2, sharex=True)
ax[0].plot(psin_lower, solver.psi_sol_lower[:, 0], label='solution from axis')
ax[0].plot(psin_upper, solver.psi_sol_upper[:, 0], label='solution from boundary')
# Plot comparison solution if it exists
validation_file = 'flux_validation_vc_{}.csv'.format(factor)
if os.path.exists(validation_file):
flux_validation = np.loadtxt(validation_file, delimiter=',')
flux_validation[:, 1] /= np.max(flux_validation[:, 1])
flux_validation[:, 1] *= np.max(solver.psi_sol_lower[:, 0])
ax[0].plot(flux_validation[:, 0], flux_validation[:, 1], linestyle='--', label='JOREK')
ax[0].set_ylabel('$\Psi_1$', fontsize=fontsize)
ax[0].legend()
ax[0].set_xlim([0.0, 1.0])
ax[1].plot(psin_lower, solver.psi_sol_lower[:, 1])
ax[1].plot(psin_upper, solver.psi_sol_upper[:, 1])
ax[1].set_ylabel('$\\frac{\partial \Psi_1}{\partial r}$', fontsize=fontsize)
ax[1].set_xlabel('$\hat \Psi$', fontsize=fontsize)
plt.show()
deltas.append(solver.delta)
gammas.append(solver.gamma)
alphas.append(1 - factor)
np.savetxt(data_output, np.asarray(deltas))
np.savetxt(gamma_output, np.asarray(gammas))
alphas = np.asarray(alphas)
deltas = np.asarray(deltas)
gammas = np.asarray(gammas)
# Plot gammas
gammas_jor = np.asarray([0.000112257, 7.25606e-5, 3.87257e-5, 2.29265e-5, 1.50064e-5, 6.86054e-6, 2.586e-6])
gammas_jor /= 6.4836e-7
alphas_jor = [0.0, 0.1, 0.2, 0.25, 0.275, 0.3, 0.3125]
eta = 1e-7 * 1.9382
rho = 1e20 * 2 * 1.673 * 1e-27
gammas *= eta ** 0.6 / rho ** 0.2
fig, ax = plt.subplots(1)
ax.plot(alphas, gammas, label='Linear $\Delta\'$')
ax.scatter(alphas, gammas)
ax.plot(alphas_jor, gammas_jor, label='JOREK $\Delta\'$')
ax.scatter(alphas_jor, gammas_jor)
plt.savefig('current_stability_gammas_{}'.format(m))
ax.set_ylabel('$\gamma\ [s^{-1}]$', fontsize=fontsize)
ax.set_xlabel('$\\alpha$', fontsize=fontsize)
plt.show()
alphas_jor_8 = [0.0, 0.1, 0.2, 0.3]
gammas_8 = np.asarray([41.701, 25.616, 12.98966, 2.5974])
gammas_9 = np.asarray([6.809, 4.0393, 1.99651, 0.46058])
# Plot deltas
solver = TearingModeSolver(m, r, r_max, B_theta, B_z, j_phi, q, num_pts, delta=1e-12)
deltas_jor = gammas_jor / 0.55 / (eta / PhysicalConstants.mu_0) ** 0.6
deltas_jor /= (m * solver.r_to_B_theta(solver.r_instability) / np.sqrt(PhysicalConstants.mu_0 * rho)) ** 0.4
deltas_jor /= (solver.r_to_q_deriv(solver.r_instability) / (solver.r_instability * solver.r_to_q(solver.r_instability))) ** 0.4
deltas_jor = deltas_jor ** (5.0 / 4.0)
deltas_jor_8 = gammas_8 / 0.55 / (eta * 0.1 / PhysicalConstants.mu_0) ** 0.6
deltas_jor_8 /= (m * solver.r_to_B_theta(solver.r_instability) / np.sqrt(PhysicalConstants.mu_0 * rho)) ** 0.4
deltas_jor_8 /= (solver.r_to_q_deriv(solver.r_instability) / (solver.r_instability * solver.r_to_q(solver.r_instability))) ** 0.4
deltas_jor_8 = deltas_jor_8 ** (5.0 / 4.0)
deltas_jor_9 = gammas_9 / 0.55 / (eta * 0.01 / PhysicalConstants.mu_0) ** 0.6
deltas_jor_9 /= (m * solver.r_to_B_theta(solver.r_instability) / np.sqrt(PhysicalConstants.mu_0 * rho)) ** 0.4
deltas_jor_9 /= (solver.r_to_q_deriv(solver.r_instability) / (solver.r_instability * solver.r_to_q(solver.r_instability))) ** 0.4
deltas_jor_9 = deltas_jor_9 ** (5.0 / 4.0)
scaling = 1.05
fig, ax = plt.subplots(1)
ax.plot(alphas, deltas, label='Linear $\Delta\'$')
ax.scatter(alphas, deltas)
ax.plot(alphas_jor, deltas_jor, label='JOREK $\Delta\'$')
ax.scatter(alphas_jor, deltas_jor)
ax.plot(alphas_jor_8, deltas_jor_8, label='JOREK $\Delta\' for $\eta=10^{-8}$')
ax.scatter(alphas_jor_8, deltas_jor_8)
ax.plot(alphas_jor_8, deltas_jor_9, label='JOREK $\Delta\'$ for $\eta=10^{-9}$')
ax.scatter(alphas_jor_8, deltas_jor_9)
ax.axhline(0.0, c='k', linestyle='--')
ax.axvline(0.346, linestyle='--', color='grey', label='Linear stability boundary')
ax.axvline(0.3125, linestyle='--', color='g', label='JOREK stability boundary')
ax.axvline(0.325, linestyle='--', color='g')
ax.fill_betweenx(scaling * deltas, 0.3125, 0.325, facecolor='green', alpha=0.2)
ax.set_ylabel('$\Delta\'$', fontsize=fontsize)
ax.set_xlabel('$\\alpha$', fontsize=fontsize)
ax.set_xlim([0.0, 1.0])
ax.set_ylim([scaling * min(deltas), scaling * max(deltas)])
ax.grid(linestyle='--')
ax.legend()
plt.savefig('current_stability_deltas_{}'.format(m))
plt.show()
def compare_matsuoka(plot_results=True):
current_factors = [0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
# Get profiles
dat = np.loadtxt(os.path.join('input_profiles.dat'))
# Modify and plot input profiles
r = dat[:, 0]
R = dat[:, 1]
j_phi = dat[:, 2]
B_z = dat[:, 3]
B_theta = dat[:, 4]
psi_n = dat[:, 5]
r_to_psin = interpolate.interp1d(r, psi_n)
psin_to_r = interpolate.interp1d(r, psi_n)
r_max = r[-1]
alphas = list()
deltas_wesson = list()
deltas_matsuoka = list()
for current_factor in current_factors:
j_phi_plasma = j_phi * current_factor
j_phi_external = j_phi * (1 - current_factor)
# Integrate B_pol for j_plasma and j_virtual
poloidal_integrand = PhysicalConstants.mu_0 * j_phi_plasma * r
poloidal_field = integrate.cumtrapz(poloidal_integrand, r, initial=0.0)
poloidal_field[1:] /= r[1:]
q_plasma = r * B_z / (R * poloidal_field)
q_plasma[0] = q_plasma[1]
poloidal_integrand_ext = PhysicalConstants.mu_0 * j_phi_external * r
poloidal_field_ext = integrate.cumtrapz(poloidal_integrand_ext,
r,
initial=0.0)
poloidal_field_ext[1:] /= r[1:]
q_ext = r * B_z / (R * poloidal_field_ext)
q_ext[0] = q_ext[1]
q_ext[np.isinf(q_ext)] = 1e12
B_theta = poloidal_field + poloidal_field_ext
# Smooth input profiles using splines
num_skip = 20
R_spline = interpolate.CubicSpline(r[::num_skip], R[::num_skip])
j_phi_spline = interpolate.CubicSpline(r[::num_skip],
j_phi[::num_skip])
j_phi_plasma_spline = interpolate.CubicSpline(r[::num_skip],
j_phi_plasma[::num_skip])
j_phi_ext_spline = interpolate.CubicSpline(r[::num_skip],
j_phi_external[::num_skip])
Btheta_spline = interpolate.CubicSpline(r[::num_skip],
B_theta[::num_skip])
Bz_spline = interpolate.CubicSpline(r[::num_skip], B_z[::num_skip])
q_plasma_spline = interpolate.CubicSpline(r[::num_skip],
q_plasma[::num_skip])
q_ext_spline = interpolate.CubicSpline(r[::num_skip],
q_ext[::num_skip])
R = R_spline(r)
j_phi = j_phi_spline(r)
j_phi_plasma = j_phi_plasma_spline(r)
j_phi_ext = j_phi_ext_spline(r)
B_theta = Btheta_spline(r)
B_z = Bz_spline(r)
q_plasma = q_plasma_spline(r)
q_ext = q_ext_spline(r)
q = 1 / (1 / q_plasma + 1 / q_ext)
# Plot input profiles and compare q profile for j_plasma with JOREK input
if plot_results:
fig, ax = plt.subplots(2, 2, figsize=(10, 10), sharex=True)
ax[0, 0].plot(r, B_z, c='k')
ax[0, 0].set_ylabel('$B_{\phi}$ [T]', fontsize=fontsize)
ax[1, 0].plot(r, B_theta, c='k')
ax[1, 0].set_ylabel('$B_{\\theta}$ [T]', fontsize=fontsize)
ax[1, 0].plot(r, poloidal_field)
ax[1, 0].plot(r, poloidal_field_ext)
ax[0, 1].plot(r, j_phi * 1e-3, c='k')
ax[0, 1].plot(r, j_phi_plasma * 1e-3)
ax[0, 1].plot(r, j_phi_ext * 1e-3)
ax[0, 1].set_ylabel('$j_{\phi}$ [kA]', fontsize=fontsize)
ax[1, 1].plot(r, q, c='k')
ax[1, 1].plot(r, q_plasma)
ax[1, 1].plot(r, q_ext)
ax[1, 1].set_ylabel('q', fontsize=fontsize)
ax[1, 1].set_xlabel('r [m]', fontsize=fontsize)
ax[1, 0].set_xlabel('r [m]', fontsize=fontsize)
ax[0, 0].set_xlim([0.0, 1.0])
fig.tight_layout()
plt.savefig('input_profiles')
plt.show()
wesson_solver = TearingModeSolver(m,
r,
r_max,
B_theta,
B_z,
j_phi_plasma,
q,
num_pts,
delta=1e-12)
matsuoka_solver = MatsuokaTearingModeSolver(m,
r,
r_max,
R,
B_theta,
B_z,
1 / q_plasma,
1 / q_ext,
num_pts,
delta=1e-12)
wesson_solver.find_delta(plot_output=False)
matsuoka_solver.find_delta(plot_output=False)
if plot_results:
fig, ax = plt.subplots(2, sharex=True)
for solver in [wesson_solver, matsuoka_solver]:
psin_lower = r_to_psin(solver.r_lower)
psin_upper = r_to_psin(solver.r_upper)
ax[0].plot(psin_lower,
solver.psi_sol_lower[:, 0],
label='solution from axis')
ax[0].plot(psin_upper,
solver.psi_sol_upper[:, 0],
label='solution from boundary')
ax[1].plot(psin_lower, solver.psi_sol_lower[:, 1])
ax[1].plot(psin_upper, solver.psi_sol_upper[:, 1])
ax[0].set_ylabel('$\Psi_1$', fontsize=fontsize)
ax[0].legend()
ax[0].set_xlim([0.0, 1.0])
ax[1].set_ylabel('$\\frac{\partial \Psi_1}{\partial r}$',
fontsize=fontsize)
ax[1].set_xlabel('$\hat \Psi$', fontsize=fontsize)
plt.savefig('matsuoka_comparison')
plt.show()
deltas_wesson.append(wesson_solver.delta)
deltas_matsuoka.append(matsuoka_solver.delta)
alphas.append(1 - current_factor)
deltas = np.stack(
(np.asarray(alphas[::-1]), np.asarray(deltas_wesson[::-1]),
np.asarray(deltas_matsuoka[::-1]))).transpose()
header_string = "alpha wesson matsuoka"
# np.savetxt('deltas.txt', deltas, header=header_string)
fig, ax = plt.subplots(1)
ax.plot(deltas[:, 0], deltas[:, 1], label='$\Delta\'_{Wesson}$')
ax.scatter(deltas[:, 0], deltas[:, 1])
ax.plot(deltas[:, 0], deltas[:, 2], label='$\Delta\'_{Matsuoka}$')
ax.scatter(deltas[:, 0], deltas[:, 2])
ax.set_ylabel('$\Delta\'$', fontsize=fontsize)
ax.set_xlabel('$\\alpha$', fontsize=fontsize)
ax.set_xlim([0.0, 1.0])
ax.set_ylim([-10.0, 22.0])
ax.grid(linestyle='--')
plt.legend()
plt.savefig('matsuoka_comparison')
plt.show()
def get_stability_condition(plot_results=True):
current_factors = [
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.65, 0.675, 0.6875, 0.7, 0.8, 0.9,
1.0, 1.1, 1.2, 1.3
]
colors = cm.copper(np.linspace(0.0, 1.0, len(current_factors)))
# Get profiles
dat = np.loadtxt(os.path.join('input_profiles.dat'))
# Modify and plot input profiles
r = dat[:, 0]
R = dat[:, 1]
j_phi = dat[:, 2]
B_z = dat[:, 3]
B_theta = dat[:, 4]
psi_n = dat[:, 5]
r_to_psin = interpolate.interp1d(r, psi_n)
psin_to_r = interpolate.interp1d(r, psi_n)
q = r * B_z / (R * B_theta)
q[0] = q[1]
if plot_results:
fig, ax = plt.subplots(2, 2, figsize=(10, 10), sharex=True)
ax[0, 0].plot(r, B_z, c='k')
ax[0, 0].set_ylabel('$B_{\phi}$ [T]', fontsize=fontsize)
ax[1, 0].plot(r, B_theta, c='k')
ax[1, 0].set_ylabel('$B_{\\theta}$ [T]', fontsize=fontsize)
for i, factor in enumerate(current_factors[::-1]):
linestyle = '--' if i > 0 else '-'
ax[0, 1].plot(r,
factor * j_phi * 1e-3,
linestyle=linestyle,
c=colors[i])
ax[0, 1].set_ylabel('$j_{p}$ [kA]', fontsize=fontsize)
ax[1, 1].plot(r, q, c='k')
ax[1, 1].set_ylabel('q', fontsize=fontsize)
ax[1, 1].set_xlabel('r [m]', fontsize=fontsize)
ax[1, 0].set_xlabel('r [m]', fontsize=fontsize)
ax[0, 0].set_xlim([0.0, 1.0])
fig.tight_layout()
plt.savefig('input_profiles')
plt.show()
r_max = r[-1]
deltas = list()
gammas = list()
alphas = list()
current = np.zeros((len(current_factors), 3))
if os.path.exists(data_output):
alphas = 1 - np.asarray(current_factors)
deltas = np.loadtxt(data_output)
gammas = np.loadtxt(gamma_output)
for i, factor in enumerate(current_factors):
j_phi_sim = j_phi * (1 - factor)
solver = TearingModeSolver(m,
r,
r_max,
B_theta,
B_z,
j_phi_sim,
q,
num_pts,
delta=1e-12)
current[i, 0] = factor
current[i, 1] = solver.r_to_j_phi(solver.r_instability)
current[i, 2] = solver.r_to_j_phi_deriv(solver.r_instability)
np.savetxt('instability_currents.dat',
current,
header='Alpha\t\tJ [A]\t\tdJ_dr [A/m]')
else:
for factor in current_factors:
j_phi_sim = j_phi * factor
solver = TearingModeSolver(m,
r,
r_max,
B_theta,
B_z,
j_phi_sim,
q,
num_pts,
delta=1e-12)
solver.find_delta(plot_output=False)
solver.get_gamma()
# Transform to psi_norm for comparison with JOREK
psin_lower = r_to_psin(solver.r_lower)
psin_upper = r_to_psin(solver.r_upper)
if plot_results:
fig, ax = plt.subplots(2, sharex=True)
ax[0].plot(psin_lower,
solver.psi_sol_lower[:, 0],
label='solution from axis')
ax[0].plot(psin_upper,
solver.psi_sol_upper[:, 0],
label='solution from boundary')
# Plot comparison solution if it exists
validation_file = 'flux_validation_vc_{}.csv'.format(factor)
if os.path.exists(validation_file):
flux_validation = np.loadtxt(validation_file)
flux_validation[:, 1] /= np.max(flux_validation[:, 1])
flux_validation[:, 1] *= np.max(solver.psi_sol_lower[:, 0])
ax[0].plot(flux_validation[:, 0],
flux_validation[:, 1],
linestyle='--',
label='JOREK')
ax[0].set_ylabel('$\Psi_1$', fontsize=fontsize)
ax[0].legend()
ax[0].set_xlim([0.0, 1.0])
ax[1].plot(psin_lower, solver.psi_sol_lower[:, 1])
ax[1].plot(psin_upper, solver.psi_sol_upper[:, 1])
ax[1].set_ylabel('$\\frac{\partial \Psi_1}{\partial r}$',
fontsize=fontsize)
ax[1].set_xlabel('$\hat \Psi$', fontsize=fontsize)
plt.show()
deltas.append(solver.delta)
gammas.append(solver.gamma)
alphas.append(1 - factor)
alphas = np.stack(
(np.asarray(alphas[::-1]), np.asarray(deltas[::-1]))).transpose()
gammas = np.stack(
(np.asarray(alphas[::-1]), np.asarray(gammas[::-1]))).transpose()
np.savetxt(data_output, alphas)
np.savetxt(gamma_output, gammas)
# Load JOREK gammas
alphas_jor = [
-0.3, -0.2, -0.1, 0.0, 0.1, 0.2, 0.25, 0.275, 0.3, 0.3125, 0.325,
0.3375
]
gammas_jor = np.asarray([
0.000305073, 0.000216954, 0.000154881, 0.000110055, 7.14455e-5,
3.94265e-5, 2.48401e-5, 1.77428e-5, 1.0663e-5, 7.15803e-6, 3.77522e-6,
9.28732e-7
])
gammas_jor /= 6.4836e-7
np.savetxt(
'gammas_jor_vs_alpha.dat',
np.stack((np.asarray(alphas_jor), np.asarray(gammas_jor))).transpose())
alphas_jor_8 = [0.0, 0.1, 0.2, 0.3]
gammas_8 = np.asarray([41.701, 25.616, 12.98966, 2.5974])
gammas_9 = np.asarray([6.809, 4.0393, 1.99651, 0.46058])
# Load tm1 data
tm1_data = np.loadtxt('gammas_tm1_vs_alpha.dat')
# Multiply normalised solver gamma by density and resistivity
eta = 1e-7 * 1.9382
rho = 1e20 * 2 * 1.673 * 1e-27
gammas[:, 1] *= eta**0.6 / rho**0.2
np.savetxt('gammas_vs_alpha_si.dat', gammas)
# Plot gammas
fig, ax = plt.subplots(2, sharex=True)
ax[0].plot(gammas[:, 0], gammas[:, 1], label='Linear')
ax[0].scatter(gammas[:, 0], gammas[:, 1])
ax[0].plot(alphas_jor, gammas_jor, label='JOREK')
ax[0].scatter(alphas_jor, gammas_jor)
ax[0].plot(tm1_data[:, 0], tm1_data[:, 1], label='TM1')
ax[0].scatter(tm1_data[:, 0], tm1_data[:, 1])
ax[0].set_ylabel('$\gamma\ [s^{-1}]$', fontsize=fontsize)
ax[0].set_xlim([0.0, 1.0])
ax[0].set_ylim([0.0, 250.0])
ax[0].legend()
gammas_interp = interpolate.interp1d(gammas[:, 0], gammas[:, 1])
gammas_tm1_interp = interpolate.interp1d(tm1_data[:, 0], tm1_data[:, 1])
ax[1].plot(alphas_jor,
100 * np.abs(gammas_jor - gammas_interp(alphas_jor)) /
gammas_interp(alphas_jor),
label='JOREK vs. Linear',
c='orange')
ax[1].scatter(alphas_jor,
100 * np.abs(gammas_jor - gammas_interp(alphas_jor)) /
gammas_interp(alphas_jor),
c='orange')
ax[1].plot(tm1_data[:, 0],
100 * np.abs(tm1_data[:, 1] - gammas_interp(tm1_data[:, 0])) /
gammas_interp(tm1_data[:, 0]),
label='TM1 vs. Linear',
c='g')
ax[1].scatter(tm1_data[:, 0],
100 *
np.abs(tm1_data[:, 1] - gammas_interp(tm1_data[:, 0])) /
gammas_interp(tm1_data[:, 0]),
c='g')
skipped_index_low = 3
skipped_index_high = -3
ax[1].plot(
alphas_jor[skipped_index_low:skipped_index_high],
100 * np.abs(gammas_jor[skipped_index_low:skipped_index_high] -
gammas_tm1_interp(
alphas_jor[skipped_index_low:skipped_index_high])) /
gammas_tm1_interp(alphas_jor[skipped_index_low:skipped_index_high]),
label='TM1 vs. JOREK',
c='r')
ax[1].scatter(
alphas_jor[skipped_index_low:skipped_index_high],
100 * np.abs(gammas_jor[skipped_index_low:skipped_index_high] -
gammas_tm1_interp(
alphas_jor[skipped_index_low:skipped_index_high])) /
gammas_tm1_interp(alphas_jor[skipped_index_low:skipped_index_high]),
c='r')
ax[1].set_ylabel('Relative difference $[\%]$', fontsize=fontsize)
ax[1].set_xlabel('$\\alpha$', fontsize=fontsize)
ax[1].set_xlim([0.0, 0.4])
plt.savefig('current_stability_gammas_{}'.format(m))
plt.show()
# Get equivalent JOREK and TM1 delta
solver = TearingModeSolver(m,
r,
r_max,
B_theta,
B_z,
j_phi,
q,
num_pts,
delta=1e-12)
deltas_jor = gammas_jor / 0.55 / (eta / PhysicalConstants.mu_0)**0.6
deltas_jor /= (m * solver.r_to_B_theta(solver.r_instability) /
np.sqrt(PhysicalConstants.mu_0 * rho))**0.4
deltas_jor /= (
solver.r_to_q_deriv(solver.r_instability) /
(solver.r_instability * solver.r_to_q(solver.r_instability)))**0.4
deltas_jor = deltas_jor**(5.0 / 4.0)
deltas_jor_8 = gammas_8 / 0.55 / (eta * 0.1 / PhysicalConstants.mu_0)**0.6
deltas_jor_8 /= (m * solver.r_to_B_theta(solver.r_instability) /
np.sqrt(PhysicalConstants.mu_0 * rho))**0.4
deltas_jor_8 /= (
solver.r_to_q_deriv(solver.r_instability) /
(solver.r_instability * solver.r_to_q(solver.r_instability)))**0.4
deltas_jor_8 = deltas_jor_8**(5.0 / 4.0)
deltas_jor_9 = gammas_9 / 0.55 / (eta * 0.01 / PhysicalConstants.mu_0)**0.6
deltas_jor_9 /= (m * solver.r_to_B_theta(solver.r_instability) /
np.sqrt(PhysicalConstants.mu_0 * rho))**0.4
deltas_jor_9 /= (
solver.r_to_q_deriv(solver.r_instability) /
(solver.r_instability * solver.r_to_q(solver.r_instability)))**0.4
deltas_jor_9 = deltas_jor_9**(5.0 / 4.0)
deltas_tm1 = tm1_data[:, 1] / 0.55 / (eta / PhysicalConstants.mu_0)**0.6
deltas_tm1 /= (m * solver.r_to_B_theta(solver.r_instability) /
np.sqrt(PhysicalConstants.mu_0 * rho))**0.4
deltas_tm1 /= (
solver.r_to_q_deriv(solver.r_instability) /
(solver.r_instability * solver.r_to_q(solver.r_instability)))**0.4
deltas_tm1 = deltas_tm1**(5.0 / 4.0)
# Plot equivalent gammas
scaling = 1.05 # Factor to improve plot
fig, ax = plt.subplots(1)
ax.plot(deltas[:, 0], deltas[:, 1], label='Linear')
ax.scatter(deltas[:, 0], deltas[:, 1])
ax.plot(alphas_jor, deltas_jor, label='JOREK')
ax.scatter(alphas_jor, deltas_jor)
# ax.plot(alphas_jor_8, deltas_jor_8, label='JOREK $\Delta\'$ for $\eta=10^{-8}$')
# ax.scatter(alphas_jor_8, deltas_jor_8)
# ax.plot(alphas_jor_8, deltas_jor_9, label='JOREK $\Delta\'$ for $\eta=10^{-9}$')
# ax.scatter(alphas_jor_8, deltas_jor_9)
ax.plot(tm1_data[:, 0], deltas_tm1, label='TM1')
ax.scatter(tm1_data[:, 0], deltas_tm1)
ax.axhline(0.0, c='k', linestyle='--')
ax.axvline(0.358,
linestyle='--',
color='grey',
label='Linear stability boundary')
ax.axvline(0.3375,
linestyle='--',
color='g',
label='JOREK stability boundary')
ax.axvline(0.35, linestyle='--', color='g')
ax.fill_betweenx(scaling * deltas[:, 1],
0.3375,
0.35,
facecolor='green',
alpha=0.2)
ax.set_ylabel('$\Delta\'$', fontsize=fontsize)
ax.set_xlabel('$\\alpha$', fontsize=fontsize)
ax.set_xlim([0.0, 1.0])
ax.set_ylim([scaling * min(deltas[:, 1]), 22.0])
ax.grid(linestyle='--')
ax.legend()
plt.savefig('current_stability_deltas_{}'.format(m))
plt.show()
def get_ffp_stability_condition_with_vc(plot_results=True):
ffp_factors = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
# Modify and plot input profiles
dat = np.loadtxt(os.path.join('FFp_profiles', 'input_profiles_0.0.dat'))
r = dat[:, 0]
R = dat[:, 1]
j_phi = dat[:, 2]
B_z = dat[:, 3]
B_theta = dat[:, 4]
psi_n = dat[:, 5]
r_to_psin = interpolate.interp1d(r, psi_n)
q = r * B_z / (R * B_theta)
q[0] = q[1]
if plot_results:
fig, ax = plt.subplots(2, 2, sharex=True)
ax[0, 0].plot(r, B_z)
ax[0, 0].set_ylabel('B_tor')
ax[1, 0].plot(r, B_theta)
ax[1, 0].set_ylabel('B_theta')
ax[0, 1].plot(r, j_phi)
ax[0, 1].set_ylabel('j_phi')
ax[1, 1].plot(r, q)
ax[1, 1].set_ylabel('q')
ax[0, 0].set_xlim([0.0, 1.0])
plt.show()
r_max = r[-1]
deltas = list()
alphas = list()
for factor in ffp_factors:
# Update only j_phi to represent virtual current
dat = np.loadtxt(
os.path.join('FFp_profiles',
'input_profiles_{}.dat'.format(factor)))
j_phi = dat[:, 2]
solver = TearingModeSolver(m,
r,
r_max,
B_theta,
B_z,
j_phi,
q,
num_pts,
delta=1e-12)
solver.find_delta(plot_output=False)
psin_lower = r_to_psin(solver.r_lower)
psin_upper = r_to_psin(solver.r_upper)
if plot_results:
fig, ax = plt.subplots(2, sharex=True)
ax[0].plot(psin_lower, solver.psi_sol_lower[:, 0])
ax[0].plot(psin_upper, solver.psi_sol_upper[:, 0])
ax[0].set_ylabel('$\Psi$')
ax[0].set_xlabel('$\hat \Psi$')
ax[0].set_xlim([0.0, 1.0])
ax[1].plot(psin_lower, np.abs(solver.psi_sol_lower[:, 1]))
ax[1].plot(psin_upper, np.abs(solver.psi_sol_upper[:, 1]))
ax[1].set_ylabel('$\\frac{\partial \Psi}{\partial r}$')
ax[1].set_xlabel('$\hat \Psi$')
plt.show()
deltas.append(solver.delta)
alphas.append(1 - factor)
plt.figure()
plt.plot(alphas, deltas)
plt.axhline(0.0, linestyle='--', color='grey')
plt.ylabel('$\Delta$')
plt.xlabel('$\\alpha$')
plt.title(
'Stability profile for cylindrical plasma with locally varying FFprime'
)
plt.savefig('ffp_stability_local_vc')
plt.show()
np.savetxt('deltas_vc.dat', deltas)
def get_stability_condition(plot_results=True):
current_factors = [0.6, 0.7, 0.8, 0.9, 1.0]
colors = cm.copper(np.linspace(0.0, 1.0, len(current_factors)))
# Get profiles
dat = np.loadtxt(os.path.join('input_profiles.dat'))
# Modify and plot input profiles
r = dat[:, 0]
R = dat[:, 1]
j_phi = dat[:, 2]
B_z = dat[:, 3]
B_theta = dat[:, 4]
psi_n = dat[:, 5]
r_to_psin = interpolate.interp1d(r, psi_n)
psin_to_r = interpolate.interp1d(r, psi_n)
q = r * B_z / (R * B_theta)
q[0] = q[1]
if plot_results:
fig, ax = plt.subplots(2, 2, figsize=(10, 10), sharex=True)
ax[0, 0].plot(r, B_z, c='k')
ax[0, 0].set_ylabel('$B_{\phi}$ [T]', fontsize=fontsize)
ax[1, 0].plot(r, B_theta, c='k')
ax[1, 0].set_ylabel('$B_{\\theta}$ [T]', fontsize=fontsize)
for i, factor in enumerate(current_factors[::-1]):
linestyle = '--' if i > 0 else '-'
ax[0, 1].plot(r, factor * j_phi * 1e-3, linestyle=linestyle, c=colors[i])
ax[0, 1].set_ylabel('$j_{\phi}$ [kA]', fontsize=fontsize)
ax[1, 1].plot(r, q, c='k')
ax[1, 1].set_ylabel('q', fontsize=fontsize)
ax[1, 1].set_xlabel('r [m]', fontsize=fontsize)
ax[1, 0].set_xlabel('r [m]', fontsize=fontsize)
ax[0, 0].set_xlim([0.0, 1.0])
fig.tight_layout()
plt.savefig('input_profiles')
plt.show()
plt.figure()
for epsilon in [1e-12, 1e-8, 1e-6, 1e-4]:
r_max = r[-1]
deltas = list()
alphas = list()
for factor in current_factors:
j_phi_sim = j_phi * factor
solver = TearingModeSolver(m, r, r_max, B_theta, B_z, j_phi_sim, q, num_pts, delta=epsilon)
solver.find_delta(plot_output=False)
deltas.append(solver.delta)
alphas.append(1 - factor)
plt.plot(alphas, deltas, label="$\epsilon$={}".format(epsilon))
np.savetxt('deltas_{}.dat'.format(epsilon), np.stack((alphas, deltas), axis=-1))
plt.grid(linestyle='--')
plt.ylabel('$\Delta\'$', fontsize=fontsize)
plt.xlabel('$\\alpha$', fontsize=fontsize)
plt.legend()
plt.xlim([0.0, 1.0])
plt.savefig('current_stability_{}'.format(m))
plt.show()